Wireless communication techniques have been widely developed during the past decades due to their extensive applications. One desirable characteristic of most wireless systems is a wide bandwidth. Although there have been studies on different techniques to broaden the bandwidth of small antennas, the antenna bandwidth strictly follows the fundamental physical limit. It is well-understood that, in linear time-invariant (LTI) structures, antenna bandwidth is in contradiction with the size, and hence, small-size antennas suffer from narrow bandwidth [1-3]. This problem becomes significant when a high-rate data-transmission is required along with a very small-size antenna.
Designing ultra-wideband (UWB) antennas which are capable of transmitting high data-rate information while occupying a small volume has received attention. For instance, biomedical implants desirably have a small size while transmitting high data-rate information. Particularly, devices that interact with the nervous systems such as cochlear and visual prostheses need to transmit a large amount of data in order to provide high-resolution sensing for the user [4-6]. Even though a high data-rate can be achieved in broadband systems by increasing the carrier frequency, in low-frequency applications such as biomedical implantable devices, high-bandwidth data-transmission remains an open challenge.
Modeling the antennas by lumped-element equivalent circuit has been extensively studied. Wheeler [7] introduced the concept of LC circuit equivalence in a parallel or series arrangement for TM01 and TE01 modes, respectively. Schaubert [8] applied Prony's method to Time-Domain Reflectometer (TDR) data to synthesize a rational function with real coefficients that describes the input impedance of the antenna as the summation of poles. Schelkunoff [9] introduced a general representation of impedance functions based on an arbitrary number of resonant frequencies and developed a wideband equivalent circuit. Kim and Ling [10] used a rational-function approximation in conjunction with Cauchy method [11] to find the coefficients by using the frequency-domain data. Also, the Singularity Expansion Method (SEM) [12] and Method of Moments (MoM) [13] have been used to derive equivalent circuit for antennas. Many different approaches to find broadband equivalent. circuit for antennas have been proposed as well [14-19].